Andrey Fedotov, an official of the Russian Investigative Committee.
Detectives say the couple were "making love on the back seat when the car was parked near the lake", according to local reports.
The car had been left in "neutral gear", but their passionate movements jolted the Niva so it edged forwards into the lake near Elan.
"The lovers were shaking the car and it rolled down to the water," said a report by local news site Bloknot Volgograd.
"The young man and his girl failed to get out of the SUV in the water."
A social media posting by a friend said: "We will remember you!!! so young! Rest in peace... You are in our hearts forever..."